The Sagnac Phase Shift suggested by the Aharonov-Bohm effect for relativistic matter beams

TL;DR

This paper derives a fully relativistic expression for the Sagnac phase shift in matter beams using an analogy with the Aharonov-Bohm effect, extending Sakurai's non-relativistic approach with Cattaneo's splitting.

Contribution

It provides the first exact relativistic derivation of the Sagnac effect for matter beams, generalizing Sakurai's approximation with a self-consistent relativistic framework.

Findings

Exact relativistic formula for Sagnac phase shift derived

Sakurai's non-relativistic result recovered in first order

Method bridges non-relativistic and relativistic quantum mechanics

Abstract

The phase shift due to the Sagnac Effect, for relativistic matter beams counter-propagating in a rotating interferometer, is deduced on the bases of a a formal analogy with the the Aharonov-Bohm effect. A procedure outlined by Sakurai, in which non relativistic quantum mechanics and newtonian physics appear together with some intrinsically relativistic elements, is generalized to a fully relativistic context, using the Cattaneo's splitting technique. This approach leads to an exact derivation, in a self-consistently relativistic way, of the Sagnac effect. Sakurai's result is recovered in the first order approximation.